email: mark.dowdall@...

Hello

These are selection of the very satisfactory answers I received to my query

(detailed below) and posted this morning.

Many thanks to everyone who replied, you've been a big help.

M.Dowdall

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Question:

At the risk of sounding stupid, I need help with something that is probably

simple. I have a semi-variogram to which I have fitted a linear model. The

majority

of texts I read say that the linear model does not have a sill (and, I

assume a range?). To use this model in GEOEAS,and I quote from the manual,

"the sill must be chosen so that the corresponding

'range' parameter value will result in the desired slope". Is this not a

contadiction ???????

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Paulo.Ribeiro@...

In my opinion the problem about the "range" is a terminology one.

Instead of seen the range parameter as the distance to which the variogram

"reachs" the sill (or 95% of the sill, for models like the

exponential) I'd rather think about it as been a simple parameter of the

correlation (and/or variogram) function.

Denote the range by $\phi$, and the sill by $\sigma^2$

for the exponential model the variogram would be

$$

\gamma(h) = \sigma^2 ( 1- \exp(- \frac{h}{\phi}) )

$$

therefore the function is parametrised by $(\sigma^2, \phi)$ and $\phi$ is

the value such that $\gamma(\phi) = 0.95 * \sigma^2$

For the linear model the idea of sill does not makes sense and the

variogram model would be:

$$

\gamma(h) = \beta_0 + \beta_1 h

$$

You cannot interpret $(\beta_0, \beta_1)$ the same way you've done with

$(\sigma^2, \phi)$.

However, GEOEAS still uses the terminology "sill" and "range".

Actually, there is a much wider range of options for the variogram

function than those available in GEOEAS. For each one these things must

bee understood and checked

Concluding, I'd rather not to pay too much atttention to the usual idea of

"range" and "sill". Instead, I thing about them just as parameters of

variograms functions as for the examples above.

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benjamin.warr@...

i think that the book is using one way of 'cheating'. What they are doing is

using a spherical model to approximate a linear model. You are looking for a

constant ratio between the sill and the range which gives you a certain

slope. You then set the range and the sill to values so that to all intents

and purposes the variogram is linear within the moving neighbourhood,

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myers@...

The Truncated Linear Variogram with sill is only valid in 1-dimension and

hence standard geostatistical software will not include that model. The

programmers however are "lazy" and instead of providing a separate way to

put in the parameters for the Linear model (which does not have a sill),

they use a perhaps confusing scheme. The Linear model is defined by the

slope so they take the "sill" and the "range" and compute the quotient which

is then interpreted as the slope. That is, if you want a slope of 2, use a

range of (for example), 5 and a "sill" of 10. Think of slope as being

determined by vertical increase divided by horizontal increase.

*************************************************************************'**

jeannee@...

In some sense you're right. The choice of a parameter "slope" would be

more appropriate, but this would lead GEOEAS to manage different parameters

compared to other (stationary) models. So, for simplicity, GEOEAS asks you

to enter a sill and a range (that have no real meaning for the linear model)

just to calculate the slope of the linear model by the ratio "sill/range".

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*

Thanks again

M.Dowdall

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